On the convergence of the Generalized Finite Difference Method for solving a chemotaxis system with no chemical diffusion
This paper focuses on the numerical analysis of a discrete version of a nonlinear reaction–diffusion system consisting of an ordinary equation coupled to a quasilinear parabolic PDE with a chemotactic term. The parabolic equation of the system describes the behavior of a biological species, while th...
| Autores: | , , , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/7281 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/7281 |
| Access Level: | acceso abierto |
| Palavra-chave: | 519.6 Chemotaxis systems Generalized Finite difference Meshless method Asymptotic stability Análisis numérico 1206 Análisis Numérico |
| Resumo: | This paper focuses on the numerical analysis of a discrete version of a nonlinear reaction–diffusion system consisting of an ordinary equation coupled to a quasilinear parabolic PDE with a chemotactic term. The parabolic equation of the system describes the behavior of a biological species, while the ordinary equation defines the concentration of a chemical substance. The system also includes a logistic-like source, which limits the growth of the biological species and presents a time-periodic asymptotic behavior. We study the convergence of the explicit discrete scheme obtained by means of the generalized finite difference method and prove that the nonnegative numerical solutions in two-dimensional space preserve the asymptotic behavior of the continuous ones. Using different functions and long-time simulations, we illustrate the efficiency of the developed numerical algorithms in the sense of the convergence in space and in time. |
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